Evaluate: (854^3 − 276^3) ÷ (854^2 + 854×276 + 276^2).

Given data

• Compute (a^3 − b^3)/(a^2 + ab + b^2) with a = 854, b = 276.

Concept / Approach

• Use the identity: a^3 − b^3 = (a − b)(a^2 + ab + b^2).

Step-by-step calculation

(a^3 − b^3)/(a^2 + ab + b^2) = a − b= 854 − 276 = 578

Verification

Identity guarantees exact cancellation; no large-number expansion needed.

Common pitfalls

• Expanding cubes numerically, which is unnecessary and error-prone.

Final Answer

578